EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法

廉睿超 敬石开 李营 肖登宝 陈阳

廉睿超, 敬石开, 李营, 肖登宝, 陈阳. 考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法. 力学学报, 2022, 54(12): 3524-3537 doi: 10.6052/0459-1879-22-283
引用本文: 廉睿超, 敬石开, 李营, 肖登宝, 陈阳. 考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法. 力学学报, 2022, 54(12): 3524-3537 doi: 10.6052/0459-1879-22-283
Lian Ruichao, Jing Shikai, Li Ying, Xiao Dengbao, Chen Yang. A hybrid topology optimization method of SIMP and MMC considering precise control of minimum size. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3524-3537 doi: 10.6052/0459-1879-22-283
Citation: Lian Ruichao, Jing Shikai, Li Ying, Xiao Dengbao, Chen Yang. A hybrid topology optimization method of SIMP and MMC considering precise control of minimum size. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3524-3537 doi: 10.6052/0459-1879-22-283

考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法

doi: 10.6052/0459-1879-22-283
基金项目: 国家重点研发资助项目(2017YFB1102804)
详细信息
    作者简介:

    敬石开, 副教授, 主要研究方向: 面向增材制造的产品创新设计. E-mail: jingshikai@bit.edu.cn

  • 中图分类号: O346

A HYBRID TOPOLOGY OPTIMIZATION METHOD OF SIMP AND MMC CONSIDERING PRECISE CONTROL OF MINIMUM SIZE

  • 摘要: 拓扑优化作为一种先进设计方法, 已被成功用于多个学科领域优化问题求解, 但从拓扑优化结果到其工程应用之间仍存在诸多阻碍, 如在结构设计中存在难以制造的小孔或边界裂缝和单铰链连接等. 在拓扑优化设计阶段考虑结构最小尺寸控制是解决上述问题的一种有效手段. 在最小尺寸控制的结构拓扑优化方法中, 通用性较强的固体各向同性材料惩罚法SIMP优化结果边界模糊不光滑, 包含精确几何信息的移动变形组件法MMC对初始布局具有较强依赖性. 本文提出一种考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法. 所提方法继承了二者优势, 避免了各自缺点. 在该方法中, 首先采用活跃轮廓算法ACWE获取SIMP输出的拓扑结构边界轮廓数据, 提出了SIMP优化结果到MMC组件初始布局的映射方法. 其次, 通过引入组件的3个长度变量, 建立了半圆形末端的多变形组件拓扑描述函数模型. 最后, 以组件厚度变量为约束, 构建了考虑结构最小尺寸控制的拓扑优化模型. 采用最小柔度问题和柔性机构问题验证了所提方法的有效性. 数值结果表明, 所提方法在无需额外约束的条件下, 仅通过组件厚度变量下限设置, 可实现整体结构的最小尺寸精确控制, 并获得了具有全局光滑的拓扑结构边界.

     

  • 图  1  SIMP和MMC拓扑优化示意图

    Figure  1.  Schematic of SIMP and MMC

    图  2  悬臂梁示意图及SIMP拓扑优化结果

    Figure  2.  Schematic of the cantilever beam and the topology optimization result of SIMP

    图  3  ACWE边界识别

    Figure  3.  Boundaries identification by using the ACWE

    图  4  边界直线及平行线识别

    Figure  4.  Identification of straight lines and parallel lines

    图  5  获取组件几何信息

    Figure  5.  Obtaining the components geometry information

    图  6  悬臂梁组件映射结果

    Figure  6.  Components mapping results for a cantilever beam

    图  7  MBB梁混合拓扑优化组件映射过程

    Figure  7.  Components mapping process of MBB beam with hybrid topology optimization

    图  8  混合拓扑优化流程图

    Figure  8.  Flowchart of the hybrid topology optimization

    图  9  组件相交示意图

    Figure  9.  Schematic of incomplete intersection and overlap between components

    图  10  组件完全连接示意图

    Figure  10.  Schematic of perfectly connections between components

    图  11  半圆形末端组件示意图

    Figure  11.  Schematic of components with semicircular ends

    图  12  等厚度半圆形末端组件

    Figure  12.  Component of equal thickness with semicircular ends

    图  13  不同变量取值的半圆形末端组件

    Figure  13.  Components of semicircular ends with different variable values

    图  14  基于组件映射结果的悬臂梁优化过程

    Figure  14.  Optimization process for the cantilever beam based on components mapping results

    图  15  悬臂梁MMC拓扑优化过程

    Figure  15.  Topology optimization process of the cantilever beam using MMC

    图  16  悬臂梁不同方法优化过程的收敛历史

    Figure  16.  The iteration history of the cantilever beam using different methods

    图  17  不同最小尺寸约束下的悬臂梁混合拓扑优化结果

    Figure  17.  Hybrid topology optimization results of the cantilever beam with different minimum length scales

    图  18  最小尺寸$ {d_{\min }}{\text{ = 0}}{\text{.1}} $的悬臂梁TsSC拓扑优化结果

    Figure  18.  TsSC topology optimization result of the cantilever beam with minimum length scales $ {d_{\min }}{\text{ = 0}}{\text{.1}} $

    图  19  柔性机构示意图

    Figure  19.  Schematic of the compliant mechanism example

    图  20  柔性机构混合拓扑优化过程

    Figure  20.  Hybrid topology optimization process of the compliant mechanism

    图  21  柔性机构MMC拓扑优化过程

    Figure  21.  Topology optimization process of the compliant mechanism using MMC

    图  22  增加组件数量后的柔性机构MMC优化结果

    Figure  22.  Optimization result of the compliant mechanism using MMC after increasing the number of components

    图  23  柔性机构不同方法优化过程的收敛历史

    Figure  23.  The iteration history of the compliant mechanism using different methods

    图  24  不同最小尺寸约束下柔性机构混合拓扑优化结果

    Figure  24.  Hybrid topology optimization results of the compliant mechanism with different minimum length scales

    图  25  不同最小尺寸约束下的柔性机构TsSC拓扑优化结果

    Figure  25.  TsSC topology optimization results of the compliant mechanism with different minimum length scales

    图  26  最小尺寸$ {d_{\min }}{\text{ = 0}}{\text{.02}} $的柔性机构ECS拓扑优化结果

    Figure  26.  ECS topology optimization result of the compliant mechanism with minimum length scales $ {d_{\min }}{\text{ = 0}}{\text{.02}} $

    表  1  不同最小尺寸约束的悬臂梁目标函数

    Table  1.   Object function of the cantilever beam with different minimum length scales

    Method$ {d_{\min }} $$ \underline {{t_1}} $$ \underline {{t_2}} $$ \underline {{t_3}} $Mean compliance
    hybrid topology optimization0.160.080.080.0839.65
    0.200.100.100.1038.14
    0.240.120.120.1236.26
    TsSC0.100.050.050.0567.78
    下载: 导出CSV
  • [1] Sigmund O, Maute K. Topology optimization approaches. Structural and Multidisciplinary Optimization, 2013, 48(6): 1031-1055 doi: 10.1007/s00158-013-0978-6
    [2] Bendsøe MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197-224 doi: 10.1016/0045-7825(88)90086-2
    [3] Zhu JH, Zhang WH, Xia L. Topology optimization in aircraft and aerospace structures design. Archives of Computational Methods in Engineering, 2016, 23(4): 595-622 doi: 10.1007/s11831-015-9151-2
    [4] Shi GH, Guan CQ, Quan DL, et al. An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing. Chinese Journal Aeronautics, 2019, 33(4): 1252-1259
    [5] Baandrup M, Sigmund O, Polk H, et al. Closing the gap towards super-long suspension bridges using computational morphogenesis. Nature Communications, 2020, 11(1): 2735 doi: 10.1038/s41467-020-16599-6
    [6] Jankovics D, Barari A. Customization of automotive structural components using additive manufacturing and topology optimization. IFAC-PapersOnLine, 2019, 52(10): 212-217 doi: 10.1016/j.ifacol.2019.10.066
    [7] Jewett JL, Carstensen JV. Topology-optimized design, construction and experimental evaluation of concrete beams. Automation in Construction, 2019, 102: 59-67 doi: 10.1016/j.autcon.2019.02.001
    [8] Tian XJ, Sun XY, Liu GJ, et al. Optimization design of the jacket support structure for offshore wind turbine using topology optimization method. Ocean Engineering, 2022, 243: 110084 doi: 10.1016/j.oceaneng.2021.110084
    [9] Bendsøe MP, Sigmund O. Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 1999, 69: 635-654 doi: 10.1007/s004190050248
    [10] Bendsøe MP, Sigmund O. Topology Optimization: Theory, Methods, and Applications. Springer Science and Business Media, 2013
    [11] Xie YM, Steven GP. A simple evolutionary procedure for structural optimization. Computers and Structures, 1993, 49(5): 885-896 doi: 10.1016/0045-7949(93)90035-C
    [12] Querin OM, Young V, Steven GP, et al. Computational efficiency and validation of bi-directional evolutionary structural optimization. Computer Methods in Applied Mechanics and Engineering, 2000, 189(2): 559-573 doi: 10.1016/S0045-7825(99)00309-6
    [13] Huang X, Xie YM. Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elements in Analysis and Design, 2007, 43(14): 1039-1049 doi: 10.1016/j.finel.2007.06.006
    [14] Michael YW, Wang XM, Guo DM. A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 2003, 192(1-2): 227-246 doi: 10.1016/S0045-7825(02)00559-5
    [15] Mei YL, Wang XM. A level set method for structural topology optimization and its applications. Advances in Engineering Software, 2004, 35(7): 415-441 doi: 10.1016/j.advengsoft.2004.06.004
    [16] Guo X, Zhang WH, Zhong WL. Doing topology optimization explicitly and geometrically-a new moving morphable components based framework. Journal of Applied Mechanics, 2014, 81(8): 081009 doi: 10.1115/1.4027609
    [17] Zhang WS, Yuan J, Zhang J, et al. A new topology optimization approach based on moving morphable components (MMC) and the ersatz material model. Structural and Multidisciplinary Optimization, 2016, 53(9): 1243-1260
    [18] Zhang WS, Li D, Zhang, J, et al. Minimum length scale control in structural topology optimization based on the Moving Morphable Components (MMC) approach. Computer Methods in Applied Mechanics and Engineering, 2016, 311(1): 327-355
    [19] Sigmund O. On the design of compliant mechanisms using topology optimization. Mechanics of Structures Machines, 1997, 25(4): 493-524 doi: 10.1080/08905459708945415
    [20] Sigmund O. Morphology–based black and white filters for topology optimization. Structural and Multidisciplinary Optimization, 2007, 33(4-5): 401-424 doi: 10.1007/s00158-006-0087-x
    [21] Sigmund O. Manufacturing tolerant topology optimization. Acta Mechanica Sinica, 2009, 25(2): 227-239 doi: 10.1007/s10409-009-0240-z
    [22] Petersson J, Sigmund O. Slope constrained topology optimization. International Journal for Numerical Methods in Engineering, 1998, 41(8): 1417-1434 doi: 10.1002/(SICI)1097-0207(19980430)41:8<1417::AID-NME344>3.0.CO;2-N
    [23] Poulsen TA. A new scheme for imposing a minimum length scale in topology optimization. International Journal for Numerical Methods in Engineering, 2003, 57(6): 741-760 doi: 10.1002/nme.694
    [24] Guest JK, Prévost JH, Belytschko T. Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International Journal for Numerical Methods in Engineering, 2004, 61(2): 238-254 doi: 10.1002/nme.1064
    [25] Zhou MD, Lazarov BS, Wang FW, et al. Minimum length scale in topology optimization by geometric constraints. Computer Methods in Applied Mechanics and Engineering, 2015, 293: 266-282 doi: 10.1016/j.cma.2015.05.003
    [26] Garrido-Jurado S, Muñoz-Salinas R, Madrid-Cuevas FJ, et al. Automatic generation and detection of highly reliable fiducial markers under occlusion. Pattern Recognition, 2014, 47(6): 2280-2292 doi: 10.1016/j.patcog.2014.01.005
    [27] Li C, Kim IY, Jeswiet J. Conceptual and detailed design of an automotive engine cradle by using topology, shape, and size optimization. Structural and Multidisciplinary Optimization, 2015, 51(2): 547-564 doi: 10.1007/s00158-014-1151-6
    [28] Meng L, Zhang WH, Quan DL, et al. From topology optimization design to additive manufacturing: Today's success and tomorrow's roadmap. Archives of Computational Methods in Engineering, 2019, 27: 805-830
    [29] Wang RX, Zhang XM, Zhu BL. Imposing minimum length scale in moving morphable component (MMC)-based topology optimization using an effective connection status (ECS) control method. Computer Methods in Applied Mechanics and Engineering, 2019, 351(1): 667-693
    [30] Sun YX, Chen WW, Cai SY. An adaptive feature-driven method for structural topology optimization. Advances in Mechanical Design, 2022, 111: 2195-2209
    [31] 范慧茹. 考虑表面层异质及其不确定性的增材制造结构拓扑优化方法. [博士论文]. 大连: 大连理工大学, 2018

    Fan Huiru. Topology optimization method of additive manufacture structures with surface layer heterogeneity and uncertainty considered.[PhD Thesis]. Dalian: Dalian University of Technology, 2018 (in Chinese)
    [32] Zhang JF, Liu EH, Liao JY. An explicit and implicit hybrid method for structural topology optimization. Journal of Physics:Conference Series, 2021, 1820(1): 012283
    [33] 张军锋, 廖靖宇, 刘恩海. 基于SIMP–MMC结构尺寸精确控制拓扑优化方法. 机械强度, 2022, 44: 102-110 (Zhang Junfeng, Liao Jingyu, Liu Enhai. Topology optimization method based on SIMP–MMC for structure size precise control. Journal of Mechanical Strength, 2022, 44: 102-110 (in Chinese)
    [34] Andreassen E, Clausen A, Schevenels M, et al. Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidiplinary Optimization, 2011, 43: 1-16 doi: 10.1007/s00158-010-0594-7
    [35] Olhoff N, Bendsøe MP, Rasmussen J. On CAD–integrated structural topology and design optimization. Computer Methods in Applied Mechanics and Engineering, 1991, 89(1-3): 259-279 doi: 10.1016/0045-7825(91)90044-7
    [36] Hsu YL, Hsu MS, Chen CT. Interpreting results from topology optimization using density contours. Computers and Structures, 2001, 79(10): 1049-1058 doi: 10.1016/S0045-7949(00)00194-2
    [37] Liu ST, Li QH, Liu JH, et al. A realization method for transforming a topology optimization design into additive manufacturing structures. Engineering, 2018, 4(2): 277-285 doi: 10.1016/j.eng.2017.09.002
    [38] Chan TF, Vese LA. Active contours without edges. IEEE Transactions on Image Processing, 2001, 10(2): 266-277 doi: 10.1109/83.902291
    [39] Cui TC, Sun Z, Liu C, et al. Topology optimization of plate structures using plate element–based moving morphable component (MMC) approach. Acta Mechanica Sinica, 2020, 36(2): 412-442 doi: 10.1007/s10409-020-00944-5
  • 加载中
图(26) / 表(1)
计量
  • 文章访问数:  228
  • HTML全文浏览量:  71
  • PDF下载量:  62
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-06-22
  • 录用日期:  2022-10-17
  • 网络出版日期:  2022-10-18
  • 刊出日期:  2022-12-15

目录

    /

    返回文章
    返回